# Pierre-Louis Curien

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• ICFP
• 2000
We present the &amp;mu; -calculus, a syntax for &amp;lambda;-calculus + control operators exhibiting symmetries such as program/context and call-by-name/call-by-value. This calculus is derived from implicational Gentzen's sequent calculus <i>LK</i>, a key classical logical system in proof theory. Under the Curry-Howard correspondence between proofs and(More)
The &#955;&sgr;-calculus is a refinement of the &#955;-calculus where substitutions are manipulated explicitly. The &#955;&sgr;-calculus provides a setting for studying the theory of substitutions, with pleasant mathematical properties. It is also a useful bridge between the classical &#955;-calculus and concrete implementations.
M, M 2 . . . M . = ( .... (M1M2). . .M, 1)M, 2xl x2. . .xn.M= 2Xl.(2x2.(...(Zxn. M)... ) ). Here is a formal definition of the sets FV(M), BV(M) of free and b o u n d variables, defined by induction on M: FV(x) FV(MN) FV(Zx. M) Clearly FV(M) = B Y ( x ) = { } = FV(M) w FV(N), BV(MN) = BV(M) u BV(N) = FV(M)/{x}, BV(2x.M) = BV(M) w {x}. w B V ( M ) = V(M),(More)
• POPL
• 1993
A polymorphic function is parametric if its behavior does notdepend on the type at which it is instantiated. Starting with Reynolds'work, the study of parametricity is typically semantic. In this paper,we develop a syntactic approach to parametricity, and a formal systemthat embodies this approach: system(More)
• Mathematical Structures in Computer Science
• 1992
Pierre­Louis Curien and Giorgio Ghelli Mathematical Structures in Computer Science / Volume 2 / Issue 01 / March 1992, pp 55 ­ 91 DOI: 10.1017/S0960129500001134, Published online: 04 March 2009 Link to this article: http://journals.cambridge.org/abstract_S0960129500001134 How to cite this article: Pierre­Louis Curien and Giorgio Ghelli (1992). Coherence of(More)
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